Question

in the figure below, ( mangle jkm = 104^{circ}), ( mangle lkm = 58^{circ}), and (overline{kn}) bisects (angle lkm). find ( mangle jkn).

Explanation:

Step1: Find the measure of ∠LKN

Since \( \overline{KN} \) bisects \( \angle LKM \), by the angle - bisector definition \( m\angle LKN=\frac{1}{2}m\angle LKM \).
Given \( m\angle LKM = 58^{\circ} \), then \( m\angle LKN=\frac{1}{2}\times58^{\circ}=29^{\circ} \).

Step2: Find the measure of ∠JKN

By the angle - addition postulate \( m\angle JKN=m\angle JKM - m\angle LKN \).
Given \( m\angle JKM = 104^{\circ} \) and \( m\angle LKN = 29^{\circ} \), then \( m\angle JKN=104^{\circ}-29^{\circ} \).

Answer:

\(75\)